A direct AC power converting apparatus including a clamp circuit is disclosed in Lixiang Wei and Thomas A. Lipo, “Investigation of 9-switch dual-bridge matrix converter operating under low output power factor”, USA, IEEE, ISA 2003, vol. 1, pp. 176-181. FIG. 16 shows the direct AC power converting apparatus described in Lixiang Wei and Thomas A. Lipo, “Investigation of 9-switch dual-bridge matrix converter operating under low output power factor”. Note that for the sake of description of the present invention, reference symbols in the drawing do not necessarily correspond to those of Lixiang Wei and Thomas A. Lipo, “Investigation of 9-switch dual-bridge matrix converter operating under low output power factor”.
It is assumed here that an IPM motor is provided on an output side of this direct AC power converting apparatus. When La represents an inductance per phase which corresponds to an average value of effective inductances of the IPM motor, i represents overload current which serves as a reference for interrupting current supply to the IPM motor, Vc represents voltage between both ends of a clamp capacitor, Cc represents electrostatic capacitance of the clamp capacitor, and Vs represents line voltage of a three-phase AC power supply, and when all power stored in an inductor for three phases of the IPM motor is regenerated to the clamp capacitor, the following relational expression is satisfied.
      [          Expression      ⁢                          ⁢      1        ]                                                          1              2                        ⁢                          La              ⁡                              (                                                      i                    2                                    +                                                            (                                              i                        2                                            )                                        2                                    +                                                            (                                              i                        2                                            )                                        2                                                  )                                              =                                    1              2                        ⁢                          Cc              ⁡                              (                                                      Vc                    2                                    -                                                            (                                                                        2                                                ⁢                        Vs                                            )                                        2                                                  )                                      ⁢            Λ                                                (          1          )                    
Therefore, the voltage between both ends of the clamp capacitor is expressed by the following expression.
      [          Expression      ⁢                          ⁢      2        ]                                Vc          =                                                                                          3                    2                                    ⁢                                      La                    Cc                                    ⁢                                      i                    2                                                  +                                  2                  ⁢                                      Vs                    2                                                                        ⁢            Λ                                                (          2          )                    
FIG. 17 shows Expression (2) in graph. In other words, FIG. 17 is a graph showing the relationship between voltage between both ends and electrostatic capacitance of the clamp capacitor. For example, if the power supply voltage Vs is 400 V, the inductance La is 12 mH, the overload current i is 40 A, and the electrostatic capacitance of the clamp capacitor is 10 μF, the voltage Vc between both ends of the clamp capacitor is approximately 1,800 V. The power supply value exceeds device rating 1,200 V of a transistor and a diode with power supply voltage of 400 V class.
In order to keep the voltage Vc between both ends of the clamp capacitor at approximately 750 V or lower, the electrostatic capacitance of the clamp capacitor needs to be 200 μF or larger from Expression (2) and FIG. 17.
On the other hand, inrush current at power-on increases as the electrostatic capacitance of the clamp capacitor is increased, which will be described in detail. Here, a series circuit in which a power supply, a reactor, a resistor and a capacitor are connected in series is taken as an example of a series circuit for one phase, where L represents an inductance of the reactor, R represents a resistance value of the resistor, and C represents electrostatic capacitance of the clamp capacitor. Then, a transfer characteristic of output (current) to input (power supply voltage Vs) in the series circuit is expressed by the following expression.
      [          Expression      ⁢                          ⁢      3        ]                                            G            ⁡                          (              s              )                                =                                    ic              Vs                        =                          sC              ⁢                                                1                  /                  LC                                                                      s                    2                                    +                                      sR                    /                    L                                    +                                      1                    /                    LC                                                              ⁢              Λ                                                            (          3          )                    
The response to step input is obtained, whereby the following expression is derived.
      [          Expression      ⁢                          ⁢      4        ]                                            G            ⁡                          (              s              )                                =                                    sC              ⁢                                                1                  /                  LC                                                                      s                    2                                    +                                      sR                    /                    L                                    +                                      1                    /                    LC                                                              ⁢                              1                s                                      =                                                            1                  /                  L                                                                      s                    2                                    +                                      sR                    /                    L                                    +                                      1                    /                    LC                                                              ⁢              Λ                                                            (          4          )                    
Here, Expression (4) is subjected to inverse Laplace transform to obtain the response of current assuming that 1/L=D, R/L=E and 1/LC=F, and then the following expression is derived.
      [          Expression      ⁢                          ⁢      5        ]                                            i            ⁡                          (              t              )                                =                                    D              ω                        ⁢                          ⅇ                                                -                  σ                                ⁢                                                                  ⁢                t                                      ⁢            sin            ⁢                                                  ⁢            ω            ⁢                                                  ⁢            t            ⁢                                                  ⁢                          Λ              ⁢                                                          [                              Expression                ⁢                                                                  ⁢                6                            ]                                                            (          5          )                                                          ω            =                                                                                4                    ⁢                    F                                    -                                      E                    2                                                  2                                              ,                      σ            =                                          E                2                            ⁢              Λ                                                            (          6          )                    
F decreases as the electrostatic capacitance C of the capacitor increases, and D and E remain constant irrespective of the electrostatic capacitance C, and thus ω decreases as the electrostatic capacitance C of the capacitor increases. Accordingly, an amplitude term D/ω excluding attenuation through time increases as the electrostatic capacitance C of the capacitor increases. That is, inrush current increases along with an increase in electrostatic capacitance C of the capacitor.
When the maximum value of current is obtained assuming that a value obtained by differentiating i(t) with respect to time is 0 (i(t)'=0) from Expression (5), the following expression is derived.
      [          Expression      ⁢                          ⁢      7        ]                                t          =                                                    π                -                α                            ω                        ⁢            Λ                                                (          7          )                    
The current has the maximum value on this occasion. This maximum value is considered to be inrush current. FIG. 18 is a graph showing the relationship between inrush current (i((π−α)/ω)) and the electrostatic capacitance C.
As described above, in the case where the electrostatic capacitance of the clamp capacitor is set to 200 μF for keeping the voltage between both ends of the clamp capacitor charged with the regenerative current at approximately 750 V or lower, the maximum value (inrush current) of current reaches 150 A from Expressions (6) and (7).
U.S. Pat. No. 6,995,992, Japanese Patent Application Laid-Open No. 2006-54947, Japanese Patent Application Laid-Open No. 08-079963 and Japanese Patent Application Laid-Open No. 02-65667 disclose the technologies related to the present invention.